The discovery of the electron spin

S.A. Goudsmit

The golden jubilee of the Dutch Physical Society in April 1971
was concluded with a lecture by Samuel Goudsmit on the history of the
discovery of the electron spin. Actually, his could hardly be called
a polished lecture; it was a grandiose artistic performance, full of
wit and emotional involvement. Goudsmit, then at the end of his
scientific career, gave a very personal account of how chance and the
guidance by Ehrenfest, their far-sighted supervisor, led him and
Uhlenbeck to formulate their remarkable discovery. When, in connection
with the present book [*], the question
turned up how to discuss the early history of electron spin, my
thoughts returned to that day, nearly twenty five years ago, when I
had been impressed by Goudsmit's truly humane wisdom. After weighing
various alternatives I thought: why not let the master speak for
himself? Thus I came to translate Goudsmit's historic lecture. Its
text was not meant to be published as a paper, but Goudsmit
subsequently consented to its publication from a tape recording
[1]. Apart from a few minor changes I have tried
to present Goudsmit's very personal style by giving a literal
translation of the words spoken in Dutch. A number of references to
the papers mentioned by Goudsmit have been added.

J.H. van der Waals

Goudsmit delivering his lecture in 1971.

Today I will talk a little about history. The history of the
discovery of the electron spin by George Uhlenbeck and myself. That
is tricky; I don't like the history of physics, I have always been
against the way in which the historians wrote about it in earlier
days. Nowadays it is better; someone like Martin Klein, that is real,
he brings something new. But the earlier historians always described
physics as if it had been done by three or four people and they
forgot that these famous people could only do their work because of
the many others who also made contributions. They can't help it since
that is the way they have learnt it from the ordinary historians. You
hear about a man like Hitler .... and they forget the millions who
lent him the necessary support.

Then, today, there are other people who are interested and they
are the psychologists. They want to know why you became a physicist,
why you did all you have done, and start to interrogate you about
that. They want to know about your family, hoping that your
grandfather was a great chemist or a great mathematician, and then
they are always terribly disappointed when they come to me. Because,
when I first registered as a student in Leiden the Beadle said: "The
Rector would like to see you a moment". He took me to that room with
all those portraits of famous people and there, next to the portrait
of Hugo de Groot, hung a large painting of a famous jurist. "Here",
he says, "is your grandfather", I reply: "I have never heard of this
man". The great jurist's name being Goudsmit, my reply made him
angry. Actually, with my own family the psychologists could do
nothing. My grandfather was a tourist guide in Hotel des Indes in the
Hague, my mother had a millinery, and my father a wholesale business
in seats ...... for water closets.

What the historians forget - and also the physicists - is that in
the discoveries in physics chance, luck plays a very, very great
role. Of course, we do not always recognize this. If someone is rich
then he says "Yes, I have been clever, that is why I am rich"! And
the same is being said of some one who does something in physics
"yes, a really clever guy.....". Admittedly, there are cases like
Heisenberg, Dirac and Einstein, there are some exceptions. But for
most of us luck plays a very important role and that should not be
forgotten.

And this is relevant because, when I went to Leiden, I ended up
with Ehrenfest. Ehrenfest's classes were small and one had a very
good interaction with one's professor. And Ehrenfest was always
worried when we interrupted our classes when we had to go somewhere.
Once I had to accompany my father to Germany, because of his
business, and then Ehrenfest said: "Do you again have to interrupt
your classes?" But my father could not travel alone. Then he asked:
"Where are you going?" When I told him, he said: "Nearby is a
university and there is a spectroscopist, Paschen. You are interested
in spectroscopy (I had become interested in it through my high-school
teacher Lohuizen), go and have a look". That was important; I have
done it. I went to visit Paschen, who did not treat me as a student
but as a colleague. And he showed me the experimental set up which he
had for the study of the spectral line of ionised helium, which
entirely confirmed Sommerfeld's relativistic electron orbits. I did
not understand a bit of it. But, I think, I managed to hide my lack
of understanding and after my return to Leiden I have nicely studied
all this. One of the things which stuck to me is that in Paschen's
experiments on the helium line, its fine stucture and the
relativistic explanation, there was a forbidden component which was
obviously present. The following summer I was sent for a stay to
Paschen, and Paschen and Back have taught me the techniques of
spectroscopy. And when I talked to the theoreticians about that
forbidden component ......... but you know how theoreticians are
...... they then say: "Poor experiments". That forbidden line already
was an important milestone. I shall recount a few more of these
milestones.

If I talk in the first person, then there are two reasons. First:
lack of modesty, and second: as I tell that history, I can only speak
about my own experiences. You know, when Uhlenbeck tells the history
of spin then he tells a different story. I don't think either of us
lies. But if someone is lying then it is a little more I than he.

I was interested in spectral lines and the first thing I did ....
I found a formula for the doublets in the spectra, claiming that it
was exactly the same formula as used by Sommerfeld for the X-ray
doublets. And I told this to Ehrenfest. At that stage it was all
wrong but Ehrenfest never discouraged anyone and said: "That's nice,
we'll publish it". And there was a short little piece in
"Naturwissenschaften" and a very lengthy article in "Archives
Néerlandaises des Sciences exactes et naturelles", which was
published in Holland in french to be sure that nobody would read it.
Of course, as a young student I was very proud of it.

Now, what happened? Two and a half years later exactly the same
work was done, the very same formula, by Millikan in America, and
Koster gave a seminar about it in Leiden. Of course he did not know
that I had already done so. At the end of the seminar I said: "I have
spoken about the very same, here, two and a half years ago".

Now there is an important point I want to make. Do I have to get
recognition from the historians that I was the first? I had simply
guessed it while Millikan, when he obtained the formula, had new
experimental material which demonstrated its correctness. One did not
understand that the formula was correct, but the new experimental
data made it clear that he was the one who had the right formula. He
had reasons for it, I had simply guessed, I could not even convince
Ehrenfest, and it was published in french .....

In these days Kronig came from America and he came to Leiden; we
collaborated in spectroscopy and worked on the intensities in the
Zeeman effect for which we found the exact expressions
[2]. Of course, it was quite different from today;
there was no quantum mechanics at the time, don't forget that this
did not yet exist! One had to guess these little formulae; one
developed a feeling for them. It is just as with veterinary and human
medicine. People can tell one where it hurts, but a veterinary doctor
has to guess where it hurts. A horse or a cow cannot tell that. And
so it is with these little formulae. It is really curious ...... it
was a kind of numerology, and it is a miracle that we arrived at the
correct expressions which later could be derived by quantum
mechanics. Now, when it is derived it becomes quite simple. If one
knows some mathematics, then one can derive all those things. We had
to guess at them; I had a feeling for that. And that is the way
Kronig and I did those things.

Well, Ehrenfest soon found out that I was not a proper
theoretician and then he sent me to Amsterdam. Three days a week I
was part-time assistant with Zeeman and things were quite different
during those days. For instance, Wednesday evenings I took the train
back to Leiden and then had a feeling I ought to switch; the jokes
one heard and recounted in Amsterdam could not be used in Leiden.
That was not done; they were not proper enough. In Amsterdarn it was
quite friendly. Professor Zeeman, of course, was somewhat more formal
than I had been used to.

And I did something else at the time. The Pauli principle was
published early in 1925 [3]. I am convinced that
although it is one of the most important publications in physics, who
reads it now, of the younger generation, will find it hard to
understand. Even that one will not understand it all. And I wrote a
note in May [4] that the Pauli principle became
easier to understand when introducing different quantum numbers. The
quantum numbers I used for Pauli's principle were mL and
ms; ms being always the same, plus or minus
1/2. (In those days it was slightly different, one used 1 and 0, but
that does not really matter.) And if you used these for the Pauli
principle, then it became much simpler ......., as one does today of
course. You people don't know that such a change was necessary but
Pauli had introduced different quantum numbers. As a mathematician
said, the change amounted to a simple linear transformation - which
is trivial, mathematically trivial of course, but not so for the
understanding and in teaching.

Well, I had introduced those quantum numbers, but if I had been a
good physicist, then I would have noticed already in May 1925 that
this implied that the electron possessed spin. But I was no good
physicist, I am no good physicist and thus I did not realize this.

I sent my note to Copenhagen to get an opinion from Kramers and
Kronig; Kronig then having left for Copenhagen. I received a long
letter from Kronig about other things but he did not say anything
about my note. That did not interest him, apparently. This is another
important point, besides Paschen's forbidden line, the forbidden
fine-structure component. That was all in the spring of 1925. Then
Uhlenbeck appears on the scene.

George Uhlenbeck had interrupted his research to become tutor of
the children of the Netherlands ambassador in Rome. He must have done
this very well because one of them later made it to ambassador in
Washington, Van Rooyen. But, as Ehrenfest said: "there in Italy he
has learnt nothing of those new things, there they only know
classical physics". And George Uhlenbeck, who was there, has also
studied classical physics; when he came home in the summer Ehrenfest
said: "You should work together with him for a while, then he may
learn something about the new atomic structure and all that spectral
business". What he clearly thought, of course, was: "Perhaps I might
learn a little bit of real physics from Uhlenbeck".

Leiden 1924. From left to right: Dieke, Goudsmit,
Tinbergen, Ehrenfest, Kronig, Fermi. Note: Tinbergen later
changed from physics to economy and became the first Nobel
laureate in economy (1969).

So Uhlenbeck knew nothing about the new physics, but yet he did an
important thing for the modern physics that was to come. Ehrenfest
had written him a letter in which he said: "I have read an article by
a young man, it looks nice and one ought to try and see him". Well,
in those days, when your professor wrote you, you did it. And George
Uhlenbeck went to see that young man; the young man just came back
from Germany and was totally discouraged. He had spent a semester in
Göttingen and there they had given him a treatment: "Well that
man cannot know anything, besides being too small he never studied
anyplace worthwhile". So the young man really got discouraged and
meant to give up physics. But Uhlenbeck said: "Don't do that before
you first talk to Ehrenfest; come and see Ehrenfest." And the man
came to Leiden and stayed for two or three months with Ehrenfest, of
which I can show a picture. A well-known picture that you may have
seen before: there is that young man, Enrico Fermi. And under
Ehrenfest's encouragement it dawned on him that he really was a
competent physicist. And if you look at Fermi's career ....... those
are the days in which he really became a great physicist.

In any case, Uhlenbeck came to the Hague - where I lived and he
lived there too. I had promised to write a short article for
"Physica", then in Dutch, and I did it together with him, which was
really great. Because he knew nothing, but was so good; he asked all
those questions I had never asked, and from that collaboration to
make things clear emerged a few, as we now know, important results.
One of the first results that came out was a new interpretation of
the spectrum of hydrogen. We had Sommerfeld's hydrogen spectrum, and
for formal reasons and because I had investigated all those things,
we obtained a new interpretation of the hydrogen spectrum. The new
term scheme. I have a picture of it, but you know it because that is
what you learn today. On the left is the old Sommerfeld scheme, on
the right the real one ........... And the curious thing is that I,
because I knew all these intensity rules and so forth, had already
guessed the correct formulae. That was my contribution; that I knew
which formulae one had to take. One took the classical expressions
and instead of integral quantum numbers one put in half integral
quantum numbers and did a few other things, it was like magic, but it
nevertheless precisely fitted, and what I found so delightful - if
you really believed it - then the "forbidden" line which Paschen had
seen was not forbidden but a real spectral line which ought to be
present and that gave me a lot of fun.

And this, of course, is something I want to say again; people
don't believe it. In the beginning when you do something you never
know whether it is important or not, and we absolutely had no idea
that a new interpretation of the hydrogen spectrum was important.
Therefore, this was published in "Physica", in Dutch
[5]. We also had an article about those quantum
vectors L and S, the coupling of quantum vectors, all
that tommy rot, I don't know how you call it, and that was sent off
to the "Zeitschrift für Physik". Do you note the difference? We
did not know what was important. Everyone worked on those quantum
vectors and that was published in the "Zeitschrift für Physik".
The hydrogen spectrum was published in "Physica", but you note, this
spectrum pointed in the right direction.

The old and the new term scheme of hydrogen
[5]. The scheme shows the multiplet
splitting of the excited states of the hydrogen atom with
principal quantum number n=3, presented by Goudsmit in the
form in which it appeared in the original publications
of1926. The assignment in the current notation has been
added at the right. With the development of quantum
mechanics the notation changed. The quantum numbers L and J
now usedfor the orbital and total angular momentum,
respectively, correspond to K-1/2 and J-1/2 in the figure.
The "forbidden component" referred to by Goudsmit is of the
type 3 2P1/2--> 2
2S in which the total angular momentum is
conserved and L changes by plus or minus 1.

When the day came I had to tell Uhlenbeck about the Pauli
principle - of course using my own quantum numbers - then he said to
me: "But don't you see what this implies? It means that there is a
fourth degree of freedom for the electron. It means that the electron
has a spin, that it rotates". Now, I can also exactly tell you the
difference between Uhlenbeck and me as physicists. In those days, all
through the summer when I told Uhlenbeck about Landé and
Heisenberg, for instance, or about Paschen, then he asked: "Who is
that?" He had never heard of them, strange. And when he said: "That
means a fourth degree of freedom", then I asked him: "What is a
degree of freedom?" In any case, when he made his remark, it was luck
that I knew all these things about the spectra, and I then said:
"That fits precisely in our hydrogen scheme which we wrote about four
weeks ago. And if one now allows the electron to be magnetic with the
appropriate magnetic moment, then one can understand all those
complicated Zeeman-effects. They come out naturally, as well as the
Landé formulae and everything, it works beautifully".

And that was it: the spin; thus is was discovered, in that manner.
Of course we told Ehrenfest about it and then summer was over and I
went again to Amsterdam and various episodes followed. Naturally, I
found it wonderful, because in the formalism which I knew it fitted
perfectly. And the rigorous physics behind it I did not fathom. But
Uhlenbeck, being a good physicist, started to think about it. ......
"A charge that rotates"......? He claims that he then went to Lorentz
and that Lorentz replied: "Yes, that is very difficult because it
causes the self energy of the electron to be wrong".

And Uhlenbeck also tells you that ........ We had just written a
short article in German and given to Ehrenfest, who wanted to send it
to "Naturwissenschaften". Now it is being told that Uhlenbeck got
frightened, went to Ehrenfest and said: "Don't send it off, because
it probably is wrong; it is impossible, one cannot have an electron
that rotates at such high speed and has the right moment". And
Ehrenfest replied: "It is too late, I have sent it off already". But
I do not remember the event, I never had the idea that is was wrong
because I did not know enough. The one thing I remember is that
Ehrenfest said to me: "Well, that is a nice idea, though it may be
wrong. But you don't yet have a reputation, so you have nothing to
lose". That is the only thing I remember.

Well the note was submitted and published [6].
Directly, the next day, I received a letter from Heisenberg and he
refers to our "mutige Note" (courageous note). I did not even know we
needed courage to publish that. I wasn't courageous at all. I think I
still have Heisenberg's letter. In it he writes a formula ......... I
did not understand a bit of it. And then he says somewhere: "What
have you done with the factor 2?" Which factor? Not the slightest
notion, and the formula given without derivation.

I told you, the spin fitted nicely into the whole formalism. But,
of course, we also ought to have made a quantitative calculation of
the size of the splittings. If one believed in the spin, then the
spin can be "up" or "down", and what is the difference in energy -
does it come out correctly? We had the formulae already, but was it
possible to derive these formulae? We did not do that because we
imagined it would be very difficult. Now every beginning student does
it; what do you call him? ..... a freshman, a greenhorn? He manages,
but we didn't know how to do it, and therefore we had not done it.
Luckily we did not know, because if we had done it, then we would
have run into an error by a factor of 2. That would not have fitted,
but we did not know; all other things fitted perfectly, yet this does
not.

Well, we were discouraged but, again, it was a matter of luck.
Just in those days Lorentz celebrated the fiftieth anniversary of his
doctorate. And Bohr and Einstein and many other great scientists came
to Leiden. And Bohr had seen our note and was quite interested. Every
day we had a meeting, a get together with Bohr, Einstein and
Ehrenfest about the problem of the spin and all those things, at
Ehrenfest's home. There we learned a lot.

In passing I have to mention a typical Ehrenfest anecdote, not
such a nice one, perhaps. Lorentz lived in Haarlem and all these
celebreties, Rutherford, Madame Curie, Bohr, Einstein and very many
others travelled by train, a special train, from Leiden to Haarlem.
And the week before one of those rare fatal train accidents had
occurred and I said to Ehrenfest: "Wouldn't it be dreadful if that
train had an accident?" And Ehrenfest replied: "Yes, that would be
dreadful, but think of all the young physicists who then could get
jobs ......".

Bohr was highly optimistic, in particular when he saw that I had
already all the formulae for the fine structure. And he thought
perhaps, that it [i.e. the factor 2] is something trivial; probably
something relativistic. I have never understood the argument
precisely. When Bohr and Einstein were talking together at the
Ehrenfests', I did not understand a bit of it.

Anyway, Bohr made one mistake. Instead of Uhlenbeck he invited me
to Copenhagen, to see if I might learn something there. That did not
work, of course, and after six weeks he presented me with a
first-class railway ticket, to go back to the Hague. But in
Copenhagen there was a young man, Thomas, who was thoroughly
acquainted with the theory of relativity. While I was there he worked
out that Heisenberg's factor of two - which seemed lost - actually
represented the relativistic factor and everything was in order
[7].

The man who never cared to believe in the spin was Pauli. And then
Bohr said: "On your way home you should stop off at Hamburg and
explain the factor 2 to Pauli". I have tried to do so, but because I
did not really understand it myself I, naturally, was unable to
explain it to Pauli ....... But Pauli did not want to believe it; on
my return Einstein still was in Leiden and I had to explain it to him
too, which went even worse. I did not manage, but later I received a
postcard from Pauli that he had seen Thomas's work and that he
believed in it.

Part of a letter by L.H. Thomas to Goudsmit (25 March
1926). Reproduced from a transparency shown by Goudsmit
during his 1971 lecture. The original is presumably in the
Goudsmit archive
kept by the AIP Center for History of Physics.

Well, that would have been the end, as I thought myself. Thomas
was to return to England and wanted to travel via Holland to visit
me, so he wrote me a letter. Here is a part of that letter. I think
this represents an important point, and in particular the historians,
naturally, enjoy such a thing. The historians, they always try to
trace someone who, somewhere in a dark chest, has already hidden
Einstein's theory. But this they also found wonderful.

Now this is dead certain. If Kronig had not left Leiden and had
stayed with Ehrenfest, then things would have taken another course.
Ehrenfest would have encouraged him and said: "That you ought to
publish". With Pauli, of course, it was entirely different. But
admitting the great difference in this respect, if one looks
objectively ......... In the days that Kronig had that idea then the
new interpretation of the hydrogen spectrum did not exist,
mL and ms did not exist, and he may not have
known about these forbidden components because they did not interest
him. Thus, actually, the material that convinced people that it was
right simply did not exist. Also, Kronig was not really the first.
The first one to publish about the quantized electron - Kronig did
not do so - was Compton. For reasons that were totally erroneous, he
had said some four years before in the "Journal of the Franklin
Institute": "Perhaps there exists a quantized rotation of the
electrons". But the reasons he had given were wrong and unconvincing.

Then there was a short paper by Kennard, an American physicist,
who had slightly more convincing arguments, but insufficient to make
people believe him. Urey had thought about it but did not publish it.
When Kronig read our paper he published two articles to prove that we
were wrong; in "Nature" and in the "Proceedings of the National
Academy" in Washington ....... Therefore, I find it a little strange
if some historians say: "Kronig did it, really, you people did not do
it". That is the same historian who says .... that is merely a linear
transformation and, therefore, a trivial contribution.

That is the way the history looks and it is a somewhat curious
history. Who, precisely, should get credit for it? Such things are
not possible without also giving credit to all other people who have
contributed. But one aspect stands out which is of particular
importance for young people. First: you need not be a genius to make
an important contribution to physics because, I do admit, the
electron spin is an important contribution. That I know now, then we
did not know, but now I do. They all told me so.

Then I want to say one more thing: even if you make a minor
contribution, if it is not important, then this gives an enormous
satisfaction. Therefore I do believe that one should not always
aspire to tackle what is most important, but try to have fun working
in physics and obtain results.